metadata

license: mit
task_categories:
  - tabular-regression
language:
  - en
tags:
  - physics,
  - scientific,
  - pin,
  - physics-informed-network,
  - pde,
  - partial-differential-equations,
  - heat-equation,
  - heat,
  - equation,
pretty_name: 1D Heat Equation PDE Dataset
size_categories:
  - 1K<n<10K

heat1d-pde-dataset

This dataset contains numerical solutions of the 1D heat equation with cooling terms, designed for machine learning applications in scientific computing and physics-informed neural networks.

Dataset Description

Dataset Summary

The dataset consists of spatiotemporal solutions to the 1D heat equation with boundary conditions and a cooling term. Each sample includes initial states, final states (with and without noise), simulation parameters, and elapsed times.

Supported Tasks

PDE Solution Prediction
Parameter Inference
Physics-Informed Machine Learning
Scientific Machine Learning Benchmarking

Dataset Structure

{
    'initial_states': [N, 200],      # Initial temperature distribution
    'final_states': [N, 200],        # Final temperature distribution (with noise)
    'clean_initial_states': [N, 200], # Initial states without noise
    'clean_final_states': [N, 200],   # Final states without noise
    'parameters': [N, 3],            # [alpha, k, t_env]
    'elapsed_times': [N],            # Time between initial and final states
}

Data Fields

initial_states: Temperature distribution at t=0
final_states: Temperature distribution at t=elapsed_time
clean_initial_states: Noise-free initial states
clean_final_states: Noise-free final states
parameters:
- alpha: Thermal diffusivity [1e-5, 1e-4]
- k: Cooling coefficient [0.01, 0.1]
- t_env: Environmental temperature [15, 35]
elapsed_times: Time difference between states

Data Splits

All data is provided in the training set. Users should create their own validation/test splits.

Source Code

The dataset was generated using a finite difference solver for the heat equation:

∂T/∂t = α∂²T/∂x² - k(T - T_env)

with boundary conditions:

T(x=0, t) = temp1
T(x=L, t) = temp2

Noise Levels

Input states: 1% of temperature range
Output states: 0.5% of temperature range
Parameters: 1% of parameter values

Usage

Install the datasets library:

pip install datasets

Load the dataset:

from datasets import load_dataset

dataset = load_dataset("nicholasleland/heat1d-pde-dataset")

# Access the data
initial_states = dataset['train']['initial_states']
final_states = dataset['train']['final_states']
parameters = dataset['train']['parameters']

Dataset Creator

Nicholas Leland

Licensing Information

license: mit